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Automatic Construction of Boundary Parametrizations for Geometric Multigrid Solvers
Please always quote using this URN: urn:nbn:de:0297-zib-7240
- We present an algorithm that constructs parametrizations of boundary and interface surfaces automatically. Starting with high-resolution triangulated surfaces describing the computational domains, we iteratively simplify the surfaces yielding a coarse approximation of the boundaries with the same topological type. While simplifying we construct a function that is defined on the coarse surface and whose image is the original surface. This function allows access to the correct shape and surface normals of the original surface as well as to any kind of data defined on it. Such information can be used by geometric multigrid solvers doing adaptive mesh refinement. Our algorithm runs stable on all types of input surfaces, including those that describe domains consisting of several materials. We have used our method with success in different fields and we discuss examples from structural mechanics and biomechanics.
Author: | Oliver Sander, Rolf KrauseORCiD |
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Document Type: | ZIB-Report |
Tag: | boundary parametrization; geometry; multigrid; surface simplification |
MSC-Classification: | 65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D18 Computer graphics, image analysis, and computational geometry [See also 51N05, 68U05] |
65-XX NUMERICAL ANALYSIS / 65Nxx Partial differential equations, boundary value problems / 65N55 Multigrid methods; domain decomposition | |
Date of first Publication: | 2003/02/19 |
Series (Serial Number): | ZIB-Report (03-02) |
ZIB-Reportnumber: | 03-02 |
Published in: | Appeared in: Computing and Visualization in Science 9 (2006) 11-22 |